Finding the sixth result — Averages Aptitude Question
Finding the sixth result: The average of 11 results is 50. The average of the first six is 49 and of the last six… Answer and worked solution on CodeKairo.
- Topic: Averages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 90 seconds
Question
The average of 11 results is 50. The average of the first six is 49 and of the last six is 52. What is the sixth result?
Options
- 48
- 52
- 56
- 60
Show the answer and the worked solution
Correct answer: C. 56
Worked solution
- First six total = 294; last six total = 312; sum = 606.
- All eleven total = 550.
- The sixth result is counted twice, so it equals 606 − 550 = 56.
Answer: 56.
The idea
When two overlapping groups are given, their totals double-count the shared member. Subtracting the true total isolates it.
Shortcut. Measure from 50: the first six total −6 and the last six +12; all eleven total 0, so the sixth, counted twice, is 50 + 6 = 56.
Common trap. "52" — taking the last group's average as the sixth result; the sixth has to be found from the double count in the two group totals.